论文信息 - An Existence Theory for Pairwise Balanced Designs II. The Structure of PBD-Closed Sets and the Existence Conjectures

An Existence Theory for Pairwise Balanced Designs II. The Structure of PBD-Closed Sets and the Existence Conjectures

The most significant work to date on the Existence Conjecture is that of Hanani [3, 4, 51. It is shown that the conditions (1) and (2) are both necessary and sufficient for the existence of a (v, k, A)-BIBD when k = 3,4 and for all A. Hanani also proves that (1) and (2) are sufficient for the existence of a (v, 5, A)-BIBD with one exception: namely, no (15, 5, 2)BIBD exists. Recall that a set K of positive integers is said to be PBD-closed (or simply a cZosed set) iff K is equal to its closure B[KJ From [8, Proposition 5.21, we have

Richard M. Wilson | R. Wilson

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